Percentages Explained: What a Percentage Means

A percentage is a number of parts out of 100. The word comes from the Latin per centum, "by the hundred", and the sign % is read as "per cent". So 37% means 37 out of every 100: the fraction 37/100 or the decimal 0.37.

A hundred square makes this easy to see. It is a 10 × 10 grid of 100 equal squares, so every square is 1% of the whole. Shade 37 squares and 37% of the grid is shaded. The 63 squares left are 63%, and together the two parts make the whole grid: 37% + 63% = 100%. That is a useful check whenever a whole is split into parts: the percentages should add up to 100%.

A percentage is another way of writing a fraction or a decimal, so you can move between all three:

• Percentage to decimal: divide by 100. 45% = 0.45 and 7% = 0.07.
• Decimal to percentage: multiply by 100. 0.375 = 37.5%.
• Fraction to percentage: divide the top by the bottom, then multiply by 100. 3/8 = 0.375 = 37.5%.
• Percentage to fraction: write it over 100 and simplify. 45% = 45/100 = 9/20.

Small percentages need care with place value. 7% is seven hundredths, 0.07, not seven tenths.

A few equivalents come up so often that they are worth knowing by heart: 1/2 = 0.5 = 50%, 1/4 = 0.25 = 25%, 3/4 = 0.75 = 75%, 1/5 = 0.2 = 20% and 1/10 = 0.1 = 10%. With these, many questions can be done in your head: 25% of something is a quarter of it and 20% is a fifth. On the number line in the infographic, each percentage sits directly above its matching fraction and decimal.

To write one amount as a percentage of another, make a fraction and multiply by 100. A test score of 18 out of 24 is 18 ÷ 24 × 100 = 75%. A score of 30 out of 40 is also 75%, so the two results are equally good even though the totals are different. That is the main reason percentages are used: they put different totals on the same scale.

Both amounts must be in the same unit first. 45 cm out of 2 m is 45 cm out of 200 cm, which is 45 ÷ 200 × 100 = 22.5%.

100% is the whole amount, but percentages do not have to stop there. If a plant grows from 40 cm to 60 cm, its new height is 60 ÷ 40 = 1.5 times the old one, or 150% of it. Percentages smaller than 1% are possible too: 0.5% is half of one per cent, or 5 parts in every 1,000.

This part is about what a percentage is. The rest of the series puts the idea to work: finding a percentage of an amount, increasing and decreasing with multipliers, measuring a percentage change, telling percentages from percentage points, avoiding the most common mistakes, spotting percentages in everyday life and, finally, a quiz on all of it.